SAMOP 2023 – wissenschaftliches Programm
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QI: Fachverband Quanteninformation
QI 34: Concepts and Methods III
QI 34.6: Vortrag
Freitag, 10. März 2023, 12:15–12:30, B302
Exploiting Graph Symmetries for Quantum Dynamics Algorithmically — •Armin Johannes Römer1,2, Robert Zeier3, and Thomas Schulte-Herbrüggen1,4,5 — 1Technische Universität München (TUM) — 2Forschungszentrum Jülich GmbH, IEK-9 — 3Forschungszentrum Jülich GmbH, PGI-8 (Quantum Control) — 4Munich Center for Quantum Science and Technology (MCQST) — 5Munich Quantum Valley e.V. (MQV)
Coupled n-level systems (spins) can classically be represented as coloured graphs, where vertices relate to local spins and differently coloured edges stand for pairwise couplings of different type.
We present an efficient algorithm to exploit graph symmetries for arriving at symmetry-adapted bases. Its core scales classically with the number of spins as vertices of the graph: its input is merely the graph’s adjacency matrix, it avoids calculating the underlying graph automorphism group, and its output is a transformation matrix into a symmetry adapted basis. It connects the Weisfeiler-Leman algorithm, known from graph isomorphism problems, with cutting-edge versions of calculating central idempotents in magma.
We demonstrate how classical graph symmetry carries over to quantum Hilbert space. Worked examples illustrate principles and practice in a manner applicable to, e.g., quantum simulation, quantum dynamics, and quantum information.